Abstract
In Chap. 9, we consider the design of a nonlinear structured controller for systems that can be well described by uncertain multi-models. In a first part, the concept of multi-model is introduced and some examples are given to show how this works. After that, the problem of designing a nonlinear structured controller for a given uncertain multi-model is considered. A characterization of the set of quadratically stabilizing controllers is first introduced. This result is then used to design a nonlinear structured controller that quadratically stabilizes the uncertain multi-model, while satisfying a given performance objective. Some design examples are presented to illustrate the main points introduced in this chapter.
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Notes
- 1.
Let \(x\in\mathbf{R}^{n_{x}}\) be a vector, the Euclidean norm of x is defined as \(\|x\|=\sqrt{x^{T}x}\).
- 2.
Since \(J(\hat{f})\) is convex, this is actually a necessary and sufficient condition for global minimum.
- 3.
Note that the local model does not depend on u, and this is why the validity functions depend only on x.
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Toscano, R. (2013). Nonlinear Structured Control via the Multi-model Approach. In: Structured Controllers for Uncertain Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-5188-3_9
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DOI: https://doi.org/10.1007/978-1-4471-5188-3_9
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5187-6
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